So, the thing about comparing partner dancing to RPGs is that a naive approach would be that the lead is the GM, and the follow is the player. This is, it turns out, exactly wrong.

The follow in partner dance is the GM, with a role that encompasses pretty much everything a GM does in an RPG except for scene-setting (which is handled by whoever chooses the music). The lead's role, by contrast, is pretty much exactly like that of a player in an RPG.

The follow's job is to maintain the physics model of the dance, to add styling, and to respond to what the lead does -- but not to make directional choices in the dance itself -- just like the GM's job is to maintain the physics mode of the game, to add flavor text, and to respond to what the players do, but not, generally to set narrative direction (except by picking the scenario, which as I mentioned, is much like picking the music in that it sets the scenes, but doesn't determine character choices). A good follow will maintain a consistent physics model (momentum, etc) commensurate with the style of the dance, except when they choose to creatively depart from it or when safety becomes a factor -- just like a good GM will keep the narrative and physical logic of the game world consistent unless they have a good reason to depart from them.

The lead's job is to make clear creative choices, and to communicate them clearly and directly--just like a player's job is to make clear narrative and strategic choices for their character. In both cases, the rule is "have a plan, but be prepared to improvise."

The reason it's possible (or even likely) that people will reverse these is the assumption that both the GM and the lead are "in charge". But, of course, neither the GM nor the lead are really in charge; what people do in a group or paired activity for pleasure is a matter of consensus, however roles are divided up.